Saturn’s moon Enceladus harbours a global subsurface ocean beneath its icy crust. Tidal dissipation within the moon’s core generates a substantial amount of heat which leads to ocean convection. Observations of the moon indicate ocean thickness variations of up to 20 km from equator to pole and heterogeneous heat generation within the core likely results in latitude-dependent temperature gradients. The effects of meridional thickness variations and heterogeneous temperature gradients on rotating thermal convection have not been simulated in previous studies. Here we simulate a non-uniform spherical shell employing a degree-2 zonal thickness profile. Using direct numerical simulations, we analysed various properties associated with heat transfer behaviour for flows in a uniform and non- uniform spherical shell domain driven by thermal convection with the Rayleigh number in the range 1.6×10⁵ ≤ Ra ≤ 5.0×10⁶ and constant Ekman number of Ek = 3×10^-4 and Prandtl number of Pr = 1. Our results demonstrate that different regimes of convection exist, which depend on the relative influence of rotation. With increasing thermal forcing, convection moves from being restricted to equatorial regions to filling the whole fluid domain. Global scaling behaviour for both domains was found to be consistent with literature, although weaker polar convection in non-uniform shells caused a decrease in heat transfer efficiency and thus a diminished heat transfer scaling behaviour. The diminishing transport of heat at the poles in the non-uniform shell deviates from the predicted heat flux profile at Enceladus, suggesting that stronger thermal heterogeneities are required to enhance polar heat transfer.